1. Field of the Invention
The present invention relates to a design process of engineering product shape that optimally designs the shape of a product based on evaluation values on a performance of the product and more particularly to a design process for a cross-sectional shape of a tire for use in vehicles based on evaluation values on a performance of the tire. Also, the present invention relates to a pneumatic tire designed by use of such a design process.
2. Description of the Related Art
Conventionally, design of the structure and shape of a structural body has been mostly made by so-called trial-and-error design search in which a prototype structural body is made and its performance is evaluated by conducting experiments or performance evaluation is performed by preparing a structural analysis model of the structure and conducting numerical experiments by use of various structural analysis methods including finite element analysis, and then redesign or reproduction of the structural body or structural analysis model is performed based on the performance evaluation result. Therefore, to design an optimal structural body that the designer desires, much labor and long time as well as high cost for production of a prototype are needed.
The same is true for tire manufacturers. The designing of a tire requires much labor, time and cost since it involves preparing a prototype by trial and error and conducting numerical experiments. In particular, cross-sectional shape of a tire cut in a plane including its axis of tire rotation, i.e., tire profile (tire contor), gives a great influence on a tire performance so that a lot of consideration for designing has been particularly necessary to obtain a desired evaluation of the tire performance.
Today, an improvement in high speed processing of numerical computation by a super computer or the like has led to various proposals on an optimal design method by the numerical computation for obtaining an optimal product evaluation of a performance. The proposals are said to solve the problems mentioned above and enables efficient optimal design.
However, full advantage of the above optimal design method has not been taken in the case of a tire as a structural body due to complexity in the method of defining the tire profile.
For example, as shown by a portion A′ in FIG. 9A, optimal tire profile obtained by the optimal design method may have a bent portion. It is very difficult to practically produce a tire having such a profile using a tire vulcanizing mold and as a result the optimal tire profile obtained by optimal design could not be realized.
Generally, as shown in FIG. 9B, the tire profile is defined by the smooth inner surface shape of the tire, the smooth arranged shape of the carcass member formed as a principal member of the tire, the smooth outer surface shape of the tread portion of the tire, the smooth outer surface shape of the side portion of the tire. Also, the optimal tire profile must be defined by continual connections of plural arcs and in addition the arcs must be defined so as to be smoothly connected. For this purpose, when the optimal design method mentioned above is applied to a tire profile, many constraint conditions that constrain design variables such as the radius of curvature, arc center position and arc length must be set up such that the arcs can be connected to each other smoothly. However, it is difficult to process the constraint conditions while retaining general applicability in determining an optimal tire profile. Also, a dedicated process routine must be provided so that the optimal design method mentioned above cannot be used effectively.
On the other hand, a method for optimizing tire profile is disclosed in International Publication WO 99/07,543. According to the teaching of this publication, tire design variables (design parameters) that optimize the objective function representing the tire performance can be obtained taking into consideration the tire performance and the constraint conditions in the tire production conditions. However, application of this method has been restricted to the optimization of profile that is limited to a specified portion such as optimization of the shape of tire crown portion or optimization of the shape of tire side portion. Efficient optimization of a wide range of design such as optimization of the entire profile of the tire as not been achieved yet.
Such a problem also arises in the case of a structural body whose design variables defining its shape are complicated.